Serpentine curve

A serpentine curve is a curve whose equation is of the form $x^2y%2Ba^2y-abx=0$ , where $ab > 0$ . Equivalently, it has a parametric representation $x=a\cot(t)$ , $y=b\sin (t)\cos(t)$ . Serpentine curves were studied by L'Hospital and Huygens, and named and classified by Newton.